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x - 2.32 : 3 = 12
=> x - 18 : 3 = 12
=> x - 6 = 12
=> x = 6 + 12 = 18
a) \(x\left(x-1\right)=0\)
\(\Rightarrow x=0\) hoặc \(x-1=0\)
+) \(x=0\)
+) \(x-1=0\Rightarrow x=1\)
Vậy \(x\in\left\{0;1\right\}\)
b) \(\left(x+2\right)\left(x-4\right)=0\)
\(\Rightarrow x+2=0\) hoặc \(x-4=0\)
+) \(x+2=0\Rightarrow x=-2\)
+) \(x-4=0\Rightarrow x=4\)
Vậy \(x\in\left\{-2;4\right\}\)
c) \(x^3.x^2=2^8:2^3\)
\(\Rightarrow x^5=2^5\)
\(\Rightarrow x=2\)
Vậy \(x=2\)
d) \(3^{x-3}-3^2=2.3^2\)
\(\Rightarrow3^{x-3}=18+9\)
\(\Rightarrow3^{x-3}=27\)
\(\Rightarrow3^{x-3}=3^3\)
\(\Rightarrow x-3=3\)
\(\Rightarrow x=6\)
Vậy \(x=6\)
\(2^{x+2}-2^x=96\)
\(\Rightarrow2^x\cdot2^2-2^x=96\)
\(\Rightarrow2^x\left(2^2-1\right)=96\)
\(\Rightarrow2^x\left(4-1\right)=96\)
\(\Rightarrow2^x\cdot3=96\)
\(\Rightarrow2^x=96:3\)
\(\Rightarrow2^x=32\)
\(\Rightarrow2^x=2^5\)
\(\Rightarrow x=5\)
\(5^x+5^{x+1}=750\)
\(\Rightarrow5^x+5^x\cdot5=750\)
\(\Rightarrow5^x\left(1+5\right)=750\)
\(\Rightarrow5^x\cdot6=750\)
\(\Rightarrow5^x=750:6\)
\(\Rightarrow5^x=125\)
\(\Rightarrow5^x=5^3\)
\(\Rightarrow x=3\)
\(2^{x+3}+2^x=144\)
\(\Rightarrow2^x\cdot2^3+2^x=144\)
\(\Rightarrow2^x\left(2^3+1\right)=144\)
\(\Rightarrow2^x\cdot9=144\)
\(\Rightarrow2^x=144:9\)
\(\Rightarrow2^x=16\)
\(\Rightarrow2^x=2^4\)
\(\Rightarrow x=4\)
a)3x-1+5.3x-1=162
3x-1.1+5.3x-1=162
3x-1.(5+1)=162
3x-1.6=162
3x-1=162/6
3x-1=27
3x-1=33
Suy ra x-1=3
x=3+1=4
b)2x+3+2x=144
2x.8+2x=144
2x.8+2x.1=144
2x.(8+1)=144
2x.9=144
2x=144/9
2x=16
2x=24
Suy ra x=4
\(3^{x-3}+2.3^{x-2}+3^{x-1}=144\)
\(\Rightarrow3^{x-1}.3^{-2}+3^{x-1}.3^{-1}.2+3^{x-1}=144\)
\(\Rightarrow3^{x-1}\left(3^{-2}+3^{-1}.2+1\right)=144\)
\(\Rightarrow3^{x-1}\left(\frac{1}{9}+\frac{2}{3}+1\right)=144\)
\(\Rightarrow\frac{16}{9}.3^{x-1}=144\)
\(\Rightarrow3^{x-1}=144:\frac{16}{9}\)
\(\Rightarrow3^{x-1}=81\)
\(\Rightarrow3^{x-1}=3^4\)
\(\Rightarrow x-1=4\)
\(\Rightarrow x=5\)